Cube & Sphere Shortcuts

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Pattern Recognition

CSCA loves cube and sphere questions. Learn the standard formulas — they show up almost every paper.

Cube diagonal = s 3 Sphere volume = \frac{4}{3} π r^{3}

Don't re-derive — memorize

Cube space diag.

$s 3$

$s$ = side length. Pythagoras twice.

Cube face diag.

$s 2$

Standard 2D Pythagoras on the face

Sphere area

$4 π r^{2}$

Volume $= \frac{4}{3} π r^{3}$